1. Field of the Invention
The invention relates to multi-channel communication systems.
2. Discussion of the Related Art
This section introduces aspects that may be helpful to facilitating a better understanding of the inventions. Accordingly, the statements of this section are to be read in this light and are not to be understood as admissions about what is in the prior art or what is not in the prior art.
A variety of communication systems use multiple channels to increase data rates and/or to separate different data streams being communicated. Examples of such systems include some wireless communication systems, digital subscriber line (DSL) systems, and dense wavelength division multiplexed (DWDM) systems. In such systems, the various channels share a portion of a physical communication link so that inter-channel crosstalk can occur between the channels. For example, a DSL system transmits the DSL tone for each channel over the same twisted copper wire pair. For that reason, a transmission on one DSL tone may be detected at a DSL receiver in the frequency channel of one or more other DSL tones. Generally, the presence of inter-channel crosstalk implies that a communication transmitted to one channel may, to some extent, be received on one or more other channels.
Many multi-channel communication systems can be described by the linear crosstalk model. The linear crosstalk model defines the relationship between the transmitted and received symbols in a communication time slot by the relation:Y=H·X+Z.  (1)In eq. (1), the N-component complex vectors X, Y, and Z represent the transmitted symbol or signal, the received symbol or signal, and the noise, respectively. In particular, the k-th components Xk, Yk, and Zk of these vectors are the transmitted signal, the received signal, and the noise signal on the k-th channel. The N×N complex matrix, H, will be referred to as the channel matrix. The (k, m)-th component Hk,m describes how the physical communication link produces a signal on the k-th channel in response to a symbol being transmitted to the m-th channel. The diagonal elements of the channel matrix, H, describe direct channel couplings, and the off-diagonal elements of the channel matrix, H, describe inter-channel couplings.